Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach

Daafouz, Jamal; Riedinger, Pierre; Iung, Claude

doi:10.1109/tac.2002.804474

Cited by 1,302 publications

(771 citation statements)

References 13 publications

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“…It should be emphasized that necessary conditions of the feasibility of inequalities (12) and (15) are that π 1 2 ii A cl,i and π 1 2 ii (A cl,i + F cl,i Ω i C i ) are Schur, ∀i ∈ I N . This can be shown similarly as in [28,25], by considering the particular cases ϕ i (C i x) = Ω i C i x and ϕ i (C i x) = 0.…”

Section: Remarkmentioning

confidence: 99%

“…The inequalities (12) and (15) are Bilinear Matrix Inequalities (BMIs), if the matrix Π ∈ M d (and U i ) is a variable, but a LMIs if Π and U i are fixed. The other inequalities in proposition 2 are LMIs.…”

Section: Remarkmentioning

confidence: 99%

“…The issue of the stability and stabilization of switched systems, which has been clearly formalized in [10], has generated many contributions to the control theory literature (see [11,12,13,14,15,16] and references therein). Mainly two frameworks should be distinguished related to the nature of the switching law.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Min-switching local stabilization for discrete-time switching systems with nonlinear modes

Jungers

Gonzaga

Daafouz

2013

Nonlinear Analysis: Hybrid Systems

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This paper deals with the discrete-time switched Lur'e problem in finite domain. The aim is to provide a stabilization inside an estimate of the origin's basin of attraction, large as possible, via a suitable switching rule. The design of this switching rule is based on the min-switching policy and can be induced by sufficient conditions given by Lyapunov-Metzler inequalities. Nevertheless instead of intuitively considering a switched quadratic Lyapunov function for this approach, a suitable switched Lyapunov function including the modal nonlinearities is proposed. The assumptions required to characterize the nonlinearities are only mode-dependent sector conditions, without constraints related to the slope of the nonlinearities. An optimization problem is provided to allow the maximization of the size of the basin of attraction estimate -which may be composed of disconnected sets -under the stabilization conditions. A numerical example illustrate the efficiency of our approach and emphasize the specificities of our tools.

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Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

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Min-switching local stabilization for discrete-time switching systems with nonlinear modes

Jungers

Gonzaga

Daafouz

2013

Nonlinear Analysis: Hybrid Systems

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“…For discrete-time switched systems with arbitrary switching signals, the switched quadratic Lyapunov function approach was proposed in Daafouz, Riedinger, and Iung (2002), which, compared with the common quadratic Lyapunov function method, has the advantage of less conservativeness. A switched linear copositive Lyapunov function method was presented in Liu (2009) to analyse the stability of switched positive systems.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

Liu

Zhao

2015

International Journal of Control

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This paper addresses the stability issue of discrete-time switched systems with guaranteed dwelltime. The approach of switched homogeneous Lyapunov function of higher order is formally proposed. By means of this approach, a necessary and sufficient condition is established to check the exponential stability of the considered system. With the observation that switching signal is actually arbitrary if the dwell time is one sample time, a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals. Using the augmented argument, a necessary and sufficient exponential stability criterion is given for discretetime switched systems with delays. A numerical example is provided to show the advantages of the theoretical results.

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“…As is well-known [18,19], different definitions of stability apply to switching systems without inputs, ranging from quadratic stability to exponential stability or asymptotic stability. Moreover, a switching system may not enjoy a certain stability property under arbitrary switching, but may have this property when it is ruled by somehow restricted switching signals, such as those satisfying a minimum dwell-time or average dwell-time: i.e., the time or the average time between two consecutive switches is not smaller than a constant [20,21].…”

mentioning

confidence: 99%

Stability issues in disturbance decoupling for switching linear systems

Zattoni

2015

2015 Proceedings of the Conference on Control and Its Applications

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Disturbance decoupling -i.e., the problem of making the output of a dynamical system insensitive to undesired inputs -is a classical problem of control theory and a main concern in control applications. Hence, it has been solved for many classes of dynamical systems, considering both structural and stability requirements. As to decoupling in linear switching systems, several definitions of stability apply. The aim of this contribution is investigating different decoupling problems with progressively more stringent stability requirements: from structural decoupling to decoupling with local input-to-state stability. A convex procedure for the computation of the switching compensator is presented, based on the fact that quadratic stability under arbitrary switching guarantees global uniform asymptotic stability and the latter implies local input-to-state stability. Measurable and inaccessible disturbances are considered in a unified setting. The work is focused on discrete-time systems, although all the results hold for continuous-time systems as well, with the obvious modifications.1 Introduction. Disturbance decoupling, which is a main issue in control system design, was first solved for linear systems in the late sixties, within the geometric approach (see, e.g., [1,2] and the references therein). Since then, the problem has been reformulated for different classes of dynamical systems and, due to the peculiarities of each context, it still attracts a fair amount of research effort: e.g., nonlinear systems have recently been considered in [3], descriptor systems and systems over rings in [4], timedelay systems in [5], linear parameter varying systems in [6,7].Lately, disturbance decoupling has been tackled for switching linear systems, that are dynamical systems described by a set of linear time-invariant systemseach of them modeling a different mode of operationand a switching signal, designating the active mode at each time instant [8][9][10]. Indeed, when switching linear systems are involved, the problem of disturbance decoupling lends itself to a number of formulations, character-

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Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach

Cited by 1,302 publications

References 13 publications

Min-switching local stabilization for discrete-time switching systems with nonlinear modes

Min-switching local stabilization for discrete-time switching systems with nonlinear modes

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

Stability issues in disturbance decoupling for switching linear systems

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